SIAM/ASA Journal on Uncertainty Quantification, Volume 9, Issue 1, Page 260-279, January 2021.
Given a set of competing models of some phenomenon together with measurement data, Bayesian model selection (BMS) is a process of finding the model that is the best candidate for being the true data-generating process. BMS relies on the computation of Bayesian model evidence, which is defined as the marginal likelihood of the measurement data (i.e., the average likelihood over a model's parameter space). In this article, we introduce a new method for computing Bayesian model evidence. Our method consists of three key elements. First, all competing model functions are emulated by Gaussian processes. Model evaluations for training the Gaussian processes are chosen one by one in a sequential manner. Second, a model-time allocation strategy decides how many model evaluations are spent on each of the competing models. Third, a sequential sampling strategy selects design points in each model's parameter space. In numerical experiments, the method shows a speed-up of more than 1,000 compared to Monte Carlo estimation. While, in lower-dimensional cases, the use of Gaussian processes alone is very effective, in higher-dimensional cases, the model-time allocation strategy and the sampling strategy become more important as they focus the effort on the right model and in the right areas of the parameter domains.

中文翻译：

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贝叶斯模型证据计算的计算机实验顺序设计

SIAM / ASA不确定性量化杂志，第9卷，第1期，第260-279页，2021年1月。
给定一组具有某种现象的竞争模型以及测量数据，贝叶斯模型选择（BMS）是寻找模型的过程，该模型最适合作为真正的数据生成过程。BMS依赖贝叶斯模型证据的计算，贝叶斯模型证据被定义为测量数据的边际可能性（即，模型参数空间上的平均可能性）。在本文中，我们介绍了一种计算贝叶斯模型证据的新方法。我们的方法包括三个关键要素。首先，所有竞争模型函数均由高斯过程进行仿真。依次选择训练高斯过程的模型评估。其次，模型时间分配策略决定在每个竞争模型上花费多少模型评估。第三，顺序采样策略在每个模型的参数空间中选择设计点。在数值实验中，与蒙特卡洛估计相比，该方法显示出超过1,000的加速。虽然在低维情况下，仅使用高斯过程非常有效，但在高维情况下，模型时间分配策略和采样策略变得更加重要，因为它们将精力集中在正确的模型和正确的模型上。参数域的区域。